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The straight line through a fixed point ...

The straight line through a fixed point (2,3) intersects the coordinate axes at distinct point P and Q. If O is the origin and the rectangle OPRQ is completed then the locus of R is

A

`3x+2y=6xy`

B

`3x+2y=6`

C

`2x+3y=xy`

D

`3x+2y=xy`

Text Solution

Verified by Experts

The correct Answer is:
D

Let the point R be (h,k) .
thus `P-=(h,0) and Q-=(0,k)`
Equation of variable line `PQ is (x)/(h)+(y)/(k)=1`
Point `A(2,3)` lies on the variable line PQ
`therefore (2)/(h)+(3)/(k)=1`
or `(2)/(x)+(3)/(y)=1`
Therefore, the locus of point R is `2y+3x=xy`.
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